Role of shear modulus and statistics in the supersolidity of helium

Abstract

The first clear evidence for supersolidity in helium came from experiments in which the resonant period of a torsional oscillator decreased below ∼0.2 K, indicating that some of the solid 4He decoupled from the oscillation. More recently, shear-modulus measurements on solid 4He revealed an unexpected increase with the same dependence on temperature and 3He impurities. The similarities raised the possibility that the period drop in torsion experiments is simply due to the stiffening of the solid. Here, we report the same measurements on solid 3He, a Fermi solid instead of a Bose solid. The anomalous modulus increase found in hexagonal close-packed (hcp) 4He, is also found in hcp 3He. However, in the case of 3He, the shear modulus increase is not accompanied by a corresponding period change of the torsional oscillator. We conclude that elastic stiffening alone does not produce the changes in the torsional-oscillator period and that decoupling occurs only in a stiffened Bose solid. The first evidence of supersolidity—the potential ability of solids to move without friction—in solid 4He was obtained in torsional-oscillator experiments. But later observations raised the possibility that the characteristic frequency changes were simply due to stiffening of the solid. Now, the results from a series of experiments comparing 3He and 4He rule out that explanation.